我知道哈希表查找的平均情况是 O(1)
,但这是否包括计算给定输入的哈希值本身所需的时间?我已经尝试在谷歌上寻找答案,阅读了所有相关文档,但无法找到 Python 中内部函数 hash()
的具体实现。一些网站声称计算哈希值只需要恒定的时间,但也有人说它是 O(k)
,其中 k
是输入长度。如果您能帮助我找到正确的答案,我将不胜感激。提前感谢:)
这完全取决于被哈希的类型。以下是一些在CPython 2.7.13中进行的简单测试,但这不是唯一的选项:
>>> pprint.pprint([(i, timeit.timeit('hash(n)', setup='n="a"*{}'.format(6400*i), number=1)) for i in range(16)])
[(0, 1.9073486328125e-06),
(1, 1.6927719116210938e-05),
(2, 3.314018249511719e-05),
(3, 4.887580871582031e-05),
(4, 6.4849853515625e-05),
(5, 8.106231689453125e-05),
(6, 9.679794311523438e-05),
(7, 0.00011301040649414062),
(8, 0.00012993812561035156),
(9, 0.00014495849609375),
(10, 0.00016188621520996094),
(11, 0.0001780986785888672),
(12, 0.00019288063049316406),
(13, 0.0002090930938720703),
(14, 0.000225067138671875),
(15, 0.00024199485778808594)]
>>> pprint.pprint([(i, timeit.timeit('hash(n)', setup='n="a"*{}'.format(6400*i))) for i in range(16)])
[(0, 0.09920382499694824),
(1, 0.09032988548278809),
(2, 0.09069585800170898),
(3, 0.09006309509277344),
(4, 0.09059309959411621),
(5, 0.09033513069152832),
(6, 0.09037399291992188),
(7, 0.09031510353088379),
(8, 0.09110498428344727),
(9, 0.09074902534484863),
(10, 0.0909719467163086),
(11, 0.09081602096557617),
(12, 0.09112405776977539),
(13, 0.09091711044311523),
(14, 0.09103798866271973),
(15, 0.09085893630981445)]
number=1000000
是timeit
的默认值),它的时间复杂度会变为常数级别。>>> pprint.pprint([(i, timeit.timeit('hash(n)', setup='n=2**{}'.format(64*i))) for i in range(16)])
[(0, 0.09280180931091309),
(1, 0.09100484848022461),
(2, 0.09413909912109375),
(3, 0.09609699249267578),
(4, 0.10647201538085938),
(5, 0.1146399974822998),
(6, 0.12569880485534668),
(7, 0.1291029453277588),
(8, 0.13350296020507812),
(9, 0.1369338035583496),
(10, 0.14037799835205078),
(11, 0.14420413970947266),
(12, 0.1485278606414795),
(13, 0.15162205696105957),
(14, 0.15520405769348145),
(15, 0.15993809700012207)]
long
也是O(n),其中n是数字的宽度,因此数量级的对数。粒度是digit
的粒度,通常为2 ** 30,特别是对于较小的整数可以直接用作哈希。
其他对象将具有自己的行为,例如元组将大致汇总其内容的哈希时间。
我做了一个小测试来验证假设。结果似乎不依赖于输入长度的长短。
import datetime
x = ['a','aa','aaaaaaaaaaaaaaaaaaaaaaaaaaaa','aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa','aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa']
for i in range(len(x)):
for j in range(len(x)):
print "Checking for: " + x[i] + " " + x[j]
a = datetime.datetime.now()
h = hash((x[i],x[j]))
b = datetime.datetime.now()
c = b - a
print "Time taken : " + str(c.microseconds)
结果
Checking for: a a
Time taken : 87
Checking for: a aa
Time taken : 10
Checking for: a aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: a aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: a aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aa a
Time taken : 9
Checking for: aa aa
Time taken : 8
Checking for: aa aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaa a
Time taken : 10
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaa aa
Time taken : 8
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 8
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 11
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa a
Time taken : 10
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 8
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
Checking for: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Time taken : 9
hash()
时间复杂度不是O(k)
,其中k
是输入的长度。我尝试使用相同类型的int
输入和list
输入进行了相同的尝试,并得到了类似的结果。绝对时间肯定是不同的,但是相对时间在这里应该是有意义的吧? - Vizaglong
(现在是 int
)取决于数字的大小(基本上是以 ULONG_MAX 为底的对数,但步长更可能受缓存影响),而 list
是可变的,因此不可哈希化。 - Yann Vernierdatetime.datetime.now()
的设计是生成单调时间戳,而不是准确的时间间隔测量。更好的性能测试函数是 time.perf_counter
。另请参阅 timeit
模块,它简化了计时测试,但请记住 Yann Vernier 关于缓存的说法。 - PM 2Ring